Ruling out some kind of infection, it sounds like your neck might be the issue. You see, your hands and fingers are innervated by nerves that start from the lower neck. You may have neck pain or maybe stiffness, but maybe not. If you have DJD (which is Arthritis) or another type of arthritis, it is possible to have these symptoms.
However, simply guessing the diagnosis, won't solve the issue. You might want to try things that may help neck alignment and posture. True neck traction, a good neck pillow... If this does nothing then we should look to another possible cause.
Have you been tested for meningitis? Do you have a fever? It could be a slipped disc or compression. Do you have osteoporosis? Either of those could cause nerve damage, which could effect your arms and legs.
With the age that you are it is highly likely that you have degenerative bone problems.
To get the correct diagnosis you need to make an appointment to see your doctor so that he can assess you. The doctor may decide to take a blood test to find out if you may have an autoimmune disorder like Rheumatoid Arthritis and also send you for imaging to find out what is going on with your bones.
Because you are experiencing a "full tight feeling in your chest" I suggest you make an urgent appointment to get seen.
If you start to experience difficulty with breathing or notice blueness around your lips or your symptoms start to worsen, call the paramedics.